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312 lines
11 KiB
312 lines
11 KiB
<chapter id="using-kmplot">
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<title>Using &kmplot;</title>
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<para>&kmplot; deals with named functions, which can be specified in
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terms of Cartesian coordinates (called <quote>explicit
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functions</quote>), polar coordinates or as parametric functions. To
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enter a function, choose
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<menuchoice><guimenu>Plot</guimenu><guimenuitem>Edit
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Plots...</guimenuitem> </menuchoice>. You can also enter new functions
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in the <guilabel>Function equation</guilabel> text box in the main
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&kmplot; window. The text box can handle explicit and polar
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functions. Each function you enter must have a unique name (&ie;, a
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name that is not taken by any of the existing functions displayed in
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the list box). A function name will be automatically generated if you
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do not specify one.</para>
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<para>For more information on &kmplot; functions, see <xref
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linkend="reference"/>.
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</para>
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<screenshot>
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<screeninfo>Here is a screenshot of the &kmplot; welcome window</screeninfo>
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<mediaobject>
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<imageobject>
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<imagedata fileref="main.png" format="PNG"/>
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</imageobject>
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<textobject>
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<phrase>Screenshot</phrase>
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</textobject>
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</mediaobject>
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</screenshot>
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<sect1 id="function-types">
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<title>Function Types</title>
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<sect2 id="explicit-functions">
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<title>Explicit Functions</title>
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<para>To enter an explicit function (&ie;, a function in the form y=f(x)) into &kmplot;, just enter it in the
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following form:
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<screen>
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<userinput><replaceable>f</replaceable>(<replaceable>x</replaceable>)=<replaceable>expression</replaceable></userinput>
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</screen>
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Where:
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<itemizedlist>
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<listitem><para>
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<replaceable>f</replaceable> is the name of the function, and can be any
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string of letters and numbers you like, provided it does not start with any of
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the letters x, y or r (since these are used for parametric and polar
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functions).</para>
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</listitem>
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<listitem><para>
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<replaceable>x</replaceable> is the x-coordinate, to be used in the expression
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following the equals sign. It is in fact a dummy variable, so you can use any
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variable name you like, but the effect will be the same.</para>
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</listitem>
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<listitem>
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<para><replaceable>expression</replaceable> is the expression to be plotted,
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given in appropriate syntax for &kmplot;. See <xref linkend="math-syntax"/>.
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</para>
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</listitem>
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</itemizedlist>
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</para>
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<para>As an example, to draw the graph of y=x<superscript>2</superscript>+2x,
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enter the following into the functions dialog of &kmplot;:
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<screen>
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f(x)=x^2+2x
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</screen>
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</para>
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</sect2>
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<sect2 id="parametric-functions">
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<title>Parametric Functions</title>
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<para>Parametric functions are those in which the x and y coordinates are
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defined by separate functions of another variable, often called t. To enter a
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parametric function in &kmplot;, follow the procedure as for an explicit
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function, but prefix the name of the function describing the x-coordinate with
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the letter x, and the function describing the y-coordinate with the letter
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y. As with explicit functions, you may use any variable name you wish for the
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parameter. To draw a parametric function, you must go to <guimenu>Plot</guimenu><guimenuitem>New Parametric Plot...</guimenuitem>. A function name will be created automatic if you do not specify one.</para>
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<para>As an example, suppose you want to draw a circle, which has parametric
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equations x=sin(t), y=cos(t). In the &kmplot; functions dialog, do the
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following:
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<orderedlist>
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<listitem><para>Open the parametric plot dialog with
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<menuchoice><guimenu>Plot</guimenu><guimenuitem>New Parametric Plot...</guimenuitem>
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</menuchoice>.</para>
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</listitem>
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<listitem><para>Enter a name for the function, say,
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<userinput>circle</userinput>, in the <guilabel>Name</guilabel>
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box. The names of the x and y functions change to match this name: the
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x function becomes <guilabel>xcircle(t)</guilabel> and the y function
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becomes <guilabel>ycircle(t)</guilabel>.</para>
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</listitem>
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<listitem>
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<para>In the x and y boxes, enter the appropriate equations, &ie;,
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<guilabel>xcircle(t)=</guilabel><userinput>sin(t)</userinput> and
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<guilabel>ycircle(t)=</guilabel><userinput>cos(t)</userinput>.</para>
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</listitem>
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</orderedlist>
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Click on <guibutton>OK</guibutton> and the function will be drawn.
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</para>
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<para>You can set some further options for the plot in this dialog:
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<variablelist>
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<varlistentry>
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<term><guilabel>Hide</guilabel></term>
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<listitem>
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<para>If this option is selected, the plot is not drawn, but &kmplot;
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remembers the function definition, so you can use it to define other
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functions.</para>
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</listitem>
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</varlistentry>
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<varlistentry>
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<term><guilabel>Custom plot minimum-range</guilabel></term>
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<term><guilabel>Custom plot maximum-range</guilabel></term>
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<listitem>
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<para>If this options are selected, you can change the maximum and
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minimum values of the parameter t for which the function is plotted
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using the <guilabel>Min:</guilabel> and <guilabel>Max:</guilabel>
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boxes.</para>
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</listitem>
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</varlistentry>
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<varlistentry>
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<term><guilabel>Line width:</guilabel></term>
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<listitem>
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<para>With this option you can set the width of the line drawn on the
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plot area, in units of 0.1mm.</para>
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</listitem>
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</varlistentry>
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<varlistentry>
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<term><guilabel>Color:</guilabel></term>
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<listitem>
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<para>Click on the color box and pick a color in the dialog that
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appears. The line on the plot will be drawn in this color.</para>
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</listitem>
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</varlistentry>
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</variablelist>
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</para>
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</sect2>
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<sect2 id="polar-functions">
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<title>Entering Functions in Polar Coordinates</title>
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<para>Polar coordinates represent a point by its distance from the origin
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(usually called r), and the angle a line from the origin to the point makes
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with the x-axis (usually represented by the Greek letter theta). To enter
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functions in polar coordinates, use the menu entry
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<menuchoice><guimenu>Plot</guimenu><guimenuitem>New Polar Plot...</guimenuitem>
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</menuchoice>. In the box labeled <guilabel>r</guilabel>, complete the
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function definition, including the name of the theta variable you want
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to use, ⪚, to draw the Archimedes' spiral r=theta, enter:
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<screen>
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<userinput>
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(theta)=theta
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</userinput>
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</screen>
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so that the whole line reads <quote>r(theta)=theta</quote>. Note that
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you can use any name for the theta variable, so
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<quote>r(foo)=foo</quote> would have produced exactly the same output.
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</para>
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</sect2>
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</sect1>
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<sect1 id="combining-functions">
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<title>Combining Functions</title>
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<para>Functions can be combined to produce new ones. Simply enter the functions
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after the equals sign in an expression as if the functions were variables. For
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example, if you have defined functions f(x) and g(x), you can plot the sum of f
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and g with:
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<screen>
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<userinput>
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sum(x)=f(x)+g(x)
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</userinput>
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</screen>
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</para>
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<para>Note that you can only combine functions of the same type, ⪚ an
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explicit function cannot be combined with a polar function.</para>
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</sect1>
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<sect1 id="function-appearance">
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<title>Changing the appearance of functions</title>
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<para>To change the appearance of a function's graph on the main plot
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window, select the function in the <guilabel>Edit Plots</guilabel>
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dialog, and click on the <guibutton>Edit</guibutton> button. In the
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dialog which appears, you can change the line width in the text box,
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and the color of the function's graph by clicking on the color button
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at the bottom. If you are editing an explicit function, you will see a
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dialog with three tabs. In the first one you specify the equation of
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the function. The <guilabel>Derivatives</guilabel> tab lets you draw
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the first and second derivative to the function. With the
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<guilabel>Integral</guilabel> tab you can draw the integral of the
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function which is calculated using Euler's method. </para>
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<para>Another way to edit a function is to right click on the
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graph. In the popup menu that appears, choose
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<guibutton>Edit</guibutton></para>
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<para>For more information on the popup menu, see <xref
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linkend="popupmenu"/>.
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</para>
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</sect1>
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<sect1 id="popupmenu">
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<title>Popup menu</title>
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<para>When right-clicking on a plot function or a single-point parametric plot function a popup menu will appear.
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In the menu there are five items available:</para>
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<variablelist>
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<varlistentry>
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<term><menuchoice><guimenuitem>Hide</guimenuitem>
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</menuchoice></term>
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<listitem>
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<para>Hides the selected graph. Other plots of the graph's function will still be shown.</para>
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</listitem>
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</varlistentry>
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<varlistentry>
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<term><menuchoice><guimenuitem>Remove</guimenuitem>
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</menuchoice></term>
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<listitem>
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<para>Removes the function. All its graphs will disappear.</para>
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</listitem>
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</varlistentry>
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<varlistentry>
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<term><menuchoice><guimenuitem>Edit</guimenuitem>
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</menuchoice></term>
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<listitem>
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<para>Shows the editor dialog for the selected function.</para>
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</listitem>
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</varlistentry>
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<varlistentry>
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<term><menuchoice><guimenuitem>Copy</guimenuitem>
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</menuchoice></term>
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<listitem>
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<para>Copies the graph to another running &kmplot; instance.</para>
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</listitem>
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</varlistentry>
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<varlistentry>
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<term><menuchoice><guimenuitem>Move</guimenuitem>
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</menuchoice></term>
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<listitem>
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<para>Moves the graph to another running &kmplot; instance.</para>
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</listitem>
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</varlistentry>
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</variablelist>
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<para>For plot functions the following four items are also available:</para>
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<variablelist>
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<varlistentry>
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<term><menuchoice><guimenuitem>Get y-Value</guimenuitem>
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</menuchoice></term>
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<listitem>
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<para>Opens a dialog in which you can find the y-value corresponding to
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a specific x-value. The selected graph will be highlighted in the
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dialog. Enter an x value in the <guilabel>X:</guilabel> box, and click
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on <guibutton>Calculate</guibutton> (or press &Enter;). The corresponding y
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value will be shown under <guilabel>Y:</guilabel>.
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</para>
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</listitem>
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</varlistentry>
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<varlistentry>
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<term><menuchoice><guimenuitem>Search for Minimum Value</guimenuitem>
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</menuchoice></term>
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<listitem>
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<para>Find the minimum value of the graph in a specified range. The
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selected graph will be highlighted in the dialog that appears. Enter
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the lower and upper boundaries of the region in which you want to
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search for a minimum, and click <guibutton>Find</guibutton>. The x and
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y values at the minimum will be shown.</para>
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</listitem>
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</varlistentry>
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<varlistentry>
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<term><menuchoice><guimenuitem>Search for Maximum Value</guimenuitem>
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</menuchoice></term>
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<listitem>
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<para>This is the same as <guimenuitem>Search for Minimum
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Value</guimenuitem> above, but finds maximum values instead of minima. </para>
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</listitem>
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</varlistentry>
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<varlistentry>
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<term><menuchoice><guimenuitem>Calculate Integral</guimenuitem>
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</menuchoice></term>
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<listitem>
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<para>Select the x-values for the graph in the new dialog that appears.
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Calulates the integral and draws the area between the graph and the x-axis in the
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selected range in the color of the graph.</para>
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</listitem>
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</varlistentry>
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</variablelist>
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</sect1>
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</chapter>
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